Meuthen told the daily Die Welt that a Swiss advertising agency had provided assistance valued at nearly €90,000 while he was running for a seat in the Baden-Württemberg state parliament in 2016.
Under German law, campaign donations from non-EU countries are illegal. Switzerland, though linked to the EU through numerous treaties, is not a member of the bloc.
Meuthen, who is carrying the party's banner into European elections in May, insisted that he had not received money “either from (ad agency) Goal AG or its chief executive Alexander Segert”.
However he received in-kind donations from the firm including around €27,000 in adverts, €17,000 worth of flyers, €41,000 in billboards and €5,000 in graphic layout work.
In exchange, Meuthen said, he signed a release form allowing Goal AG to use his “photograph and personal data for advertising purposes”.
Meuthen told Welt that an oversight office in the federal parliament had
informed him that the AfD, Germany's biggest opposition party, would be fined more than €400,000 for his and another official's suspected campaign finance violations.
He said he would challenge the penalty on the grounds that the party did
not break German law as the assistance was not a donation as such and came from EU citizens living in Switzerland.
It is not the first time that the anti-Islam, anti-immigration AfD has found itself in hot water over financing.
German media revealed in November that the AfD's Lake Constance branch received 18 donations from Swiss pharmaceutical firm PWS between July and September 2017, totalling some 150,000 Swiss francs (€130,000).
The affair led prosecutors to ask parliament to lift the immunity of prominent far-right MP Alice Weidel over suspicious campaign donations.
The AfD has railed against Chancellor Angela Merkel's liberal immigration
policies and scored nearly 13 percent in the September 2017 general election.
It is currently polling at between 10 and 12 percent ahead of the European election.